"the work of people who are institutionalized or psychologically compromised according to standard clinical norms." This definition was amended to include those enduring an altered state of consciousness -- whether from marginalization or incarceration. "Self-taught art" is a category that often overlaps with outsider art, referencing artwork made without schooling that strays from the norms and styles of the time.That's an interesting echo of the early Romantics, who were of the opinion that a little madness was necessary for the creation of art. In music we don't seem to have anything resembling this kind of category currently, so let me see if I can construct one. "Outsider" composers or musicians might include Robert Schumann, incarcerated in an insane asylum towards the end of his life, perhaps gypsy musicians in Spain, Romania and Hungary living on the edges of society, some very outside the norm composers like Harry Partch and Conlon Nancarrow, one a hobo and the other a political exile.
Looking at the examples in the HuffPost article, they are rather more primitive than my musical equivalents. I think that being a true outsider musician might be more difficult because music, as a performing art, is a far more social artform. I'm sure there are composers out there who are unconnected with the greater musical world, but as such, we may not run across them as we will not hear performances of their music. Notice that most of the artists in the HuffPost article were discovered by collectors who, if they discovered a genuine "primitive" genius could profit hugely. I'm not sure there is any similar financial incentive to discovering unknown composers!
Most composers are insiders in that they tend to come from musical families (because then they get the benefits of early exposure and instruction) and attend music schools and study with members of the musical establishment. It is hard to become a composer without doing any of those things. Even a composer like John Cage who might seem to be an outsider, studied with Arnold Schoenberg and was supported by various academic institutions from time to time.
Some examples of musical "outsiders". Here is a BBC documentary on Harry Partch, appropriately titled "The Outsider":
And here is a very odd little documentary on Nancarrow:
But it would be better to simply listen to some of his player piano studies, a kind of non-electronic, electronic music. The first one is a canon in which the two voices begin with one in very quick notes and the other in very slow notes. Over the course of the piece that relationship reverses as the quick voice slows down and the slow voice speeds up. The second is a rather psychotic-sounding fugue: